Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
548 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C9×#1009 | C2 | semidirect |
| 2. C3×#63512 | C2 | semidirect |
| 3. #11721043 | C2 | semidirect |
| 4. #11720882 | C2 | semidirect |
| 5. #11720585 | C2 | semidirect |
| 6. #11720300 | C2 | semidirect |
| 7. #11720296 | C2 | semidirect |
| 18. C2×C3×D36 | C22 | semidirect |
| 20. C4×C3⋊Dic9 | C22 | semidirect |
| 21. #88532 | C22 | semidirect |
| 24. C3×#3667 | C22 | semidirect |
| 36. #63512 | D3 | semidirect |
| 45. C3×Q8×C9 | D4 | semidirect |
| 47. C3×D4×C9 | D4 | semidirect |
| 56. C9×D12 | D4 | semidirect |
| 61. C9×Dic6 | D4 | semidirect |
| 94. C2×D36 | C2×D3 | semidirect |
| 103. #3667 | C2×D3 | semidirect |
| 118. #1009 | D9 | semidirect |
| 160. Q8×C9 | #67 | semidirect |
| 170. D4×C9 | #67 | semidirect |
| 268. C3×C9 | #453 | semidirect |
| 277. C3×Q8 | #611 | semidirect |
| 291. C3×D4 | #611 | semidirect |
| 313. D12 | #611 | semidirect |
| 316. Dic6 | #611 | semidirect |
| 388. C9 | #5198 | semidirect |
| 393. Q8 | #6194 | semidirect |
| 404. D4 | #6194 | semidirect |
| 441. C3 | #10588922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#1009 | 2 |
| C3×#63512 | 2 |
| #11721043 | 2 |
| #11720882 | 2 |
| #11720585 | 2 |
| #11720300 | 2 |
| #11720296 | 2 |
| #10591665 | 3 |
| #10588922 | 3 |